When residents in places that aren’t expanding Medicaid or setting up their own health exchanges are denied insurance, the feds will tell them who to blame: their state.

Some states aren’t going along with the Affordable Care Act, and not surprisingly, the White House isn’t too happy about that. If every state expands Medicaid and sets up its own health exchange, the law will work better, the White House argues. So how can the administration convince Republican state officials who are vehemently opposed to Obamacare to come around? They’ve got a few ideas.

One, in particular, is pretty cunning. About 20 states aren’t expanding Medicaid to 138 percent of the poverty line and will have the feds run their exchanges instead of setting up their own. When residents below the poverty line in those states go to the exchange to apply for insurance—probably oblivious to the fact that they will not be covered—they’ll get a special note from the federal government that reads, “Sorry, you can’t get health insurance because your state didn’t expand Medicaid.” (The wording will likely be more diplomatic than that, but that’s the essence of it.)

The move has Republican officials rolling their eyes at what they say is a blatantly political move. “It’s not inaccurate, but it’s certainly petty,” says Tony Keck, South Carolina’s health and human services director. His state has opted not to expand Medicaid, but it is developing contingency plans to assist confused customers on Oct. 1, when the exchanges open. “They can say whatever they want when they’re on the stump, but it’s a little bit different when it’s taxpayer-funded,” he says. “When somebody calls us, we’re not going to put them through a political commercial.”

The exchange gimmick is part of the Obama administration’s broader plan to lobby even the reddest states to buy into Obamacare. The health reform law allows states to take more control of their exchanges in later years—and insurers have said they’ll push them to do it. States can also always change their minds about the Medicaid expansion, though they’ll miss out on one year of 100 percent federal funding if they don’t expand until 2015.

Making the health reform law work is crucial to Obama’s ultimate legacy, so the administration needs to win over resistant states. The U.S. Department of Health and Human Services (HHS) held a conference call with reporters in July to publicly urge leaders in Florida—where Gov. Rick Scott and the state Senate agreed to the Medicaid expansion, but the House refused—to finish the job. Florida, with its more than a million people who would qualify for expanded Medicaid, would be a big win for the administration.

“States can improve health, protect families from financial ruin, ensure doctors and hospitals get paid for the care they deliver, and boost the economy,” Paul Dioguardi, HHS director of intergovernmental and external affairs, told reporters. “We’re still hopeful that Florida will take advantage of this generous offer.”

Still, Keck says that the White House’s tactics could have the opposite effect. They make it politically harder for state officials to come around when they resort to games like the exchange message. “I’m sure if you polled nonexpansion states,” he says, “there aren’t a lot of warm and fuzzies between them and the administration.”